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Potential Theory of Lévy Processes
Author(s) -
Hawkes John
Publication year - 1979
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-38.2.335
Subject(s) - mathematics , resolvent , semigroup , potential theory , pure mathematics , kernel (algebra) , euclidean space , operator (biology) , euclidean geometry , pseudodifferential operators , space (punctuation) , discrete mathematics , algebra over a field , mathematical analysis , biochemistry , chemistry , linguistics , geometry , philosophy , repressor , transcription factor , gene
Let X be a transient Lévy process in euclidean space. In this paper we consider some aspects of the potential theory of X when the potential kernel is not necessarily absolutely continuous. First we find exactly when the resolvent operators and the semigroup operators are strong Feller operators. Next we extend the Orey–Kanda theorem on the comparison of essentially polar sets and consider some properties of the energy minimizing distributions for non‐symmetric processes. Finally we obtain results on the relationships between the classes of exceptional sets. We also give a number of examples illustrating possible kinds of behaviour of Lévy processes.